Fuzzy Rule Interpolation Toolbox for the GNU

Open-Source OCTAVE

Maen Alzubi∗, Mohammad Almseidin∗, Mohd Aaqib Lone∗ and Szilveszter Kovacs∗

∗ Department of Information Technology, University of Miskolc, H-3515 Miskolc, Hungary

∗ Email: alzubi@iit.uni-miskolc.hu, alsaudi@iit.uni-miskolc.hu, mohdaaqiblone@iit.uni-miskolc.hu, szkovacs@iit.uni-miskolc.hu

Abstract—In most fuzzy control applications (applying classical

fuzzy reasoning), the reasoning method requires a complete fuzzy rule-base, i.e all the possible observations must be covered by the antecedents of the fuzzy rules, which is not always available. Fuzzy control systems based on the Fuzzy Rule Interpolation (FRI) concept play a major role in different platforms, in case if only a sparse fuzzy rule-base is available. This cases the fuzzy model contains only the most relevant rules, without covering all the antecedent universes. The first FRI toolbox being able to handle different FRI methods was developed by Johanyak et. al. in 2006 for the MATLAB environment. The goal of this paper is to introduce some details of the adaptation of the FRI toolbox to support the GNU/OCTAVE programming language. The OCTAVE Fuzzy Rule Interpolation (OCTFRI) Toolbox is an open-source toolbox for OCTAVE programming language, providing a large functionally compatible subset of the MATLAB FRI toolbox as well as many extensions. The OCTFRI Toolbox includes functions that enable the user to evaluate Fuzzy Inference Systems (FISs) from the command line and from OCTAVE scripts, read/write FISs and OBS to/from files, and produce a graphical visualisation of both the membership functions and the FIS outputs. Future work will focus on implementing advanced fuzzy inference techniques and GUI tools.

Index Terms—Fuzzy Rule Interpolation, OCTAVE FRI Toolbox, OCTFRI Toolbox, FRI Toolbox

I. INTRODUCTION

The most research papers related to Fuzzy Rule Interpolation

(FRI) methodology are apparently created using the MATLAB

environment. Unfortunately, there is a lack of FRI toolbox

implementation in other programming languages. There are

many implementations of the classical fuzzy reasoning methods

for dense rule base systems, but the Matlab FRI toolbox [1] is

the only FRI methodology collection for sparse rule bases. It

implements a set of different methods, because up to now, there

is no common FRI methodology for handling sparse fuzzy

models. More techniques exist which follows each other’s, but

none of them is accepted as universal FRI solution. There is a

need for a toolbox in which any of these methods can be applied

and compared.

The first FRI Toolbox was implemented by Johanyak et al´

for the MATLAB environment in [1]. This special toolbox is a

collection of MATLAB FRI functions, which can be run under

MATLAB. It is easy to use and handy tool for demonstration

and research purposes, but the integration into the real

application is troublesome. Therefore, a new developer

framework which includes more FRI methods has been

designed and implemented.

This paper focuses on the use of the Fuzzy Rule Interpolation

(FRI) to support GNU/OCTAVE program. The OCTAVE

Fuzzy Rule Interpolation (OCTFRI) toolbox is an open-source

toolbox for OCTAVE that provides a large MATLAB

compatible subset of the functionality of the MATLAB FRI

toolbox as well as many extensions. The OCTFRI toolbox

includes functions that enable the user to evaluate Fuzzy

Inference Systems (FISs) from the command line and from

OCTAVE scripts, read/write FISs and OBS to/from files, and

produce a graphical output of both the membership functions

and the FIS outputs. Future work will focus on implementing

advanced fuzzy inference techniques and GUI tools. The

OCTAVE FRI toolbox is available for download on [2].

The rest of the paper is organized as follows: Section II

provides the background of the FRI toolbox. Section III

presents features of the OCTAVE FRI toolbox and its structure

and functions. Section IV introduces a summary of some

Interpolative System (FIS) types. Section V presents related

works of the FRI MATLAB toolbox. Section VI introduces the

fuzzy rule interpolation OCTAVE toolbox itself. Section VII

gives practical examples for the evaluation of two different FIS

and OBS data files. The conclusion and future work are

presented in section VIII.

II. BACKGROUND

The use of the FRI toolbox for implementing type-1 fuzzy

inference systems is no diffuse. Currently, there is a deficiency

of the FRI toolbox available for creating other types of fuzzy

systems and other programming languages. As mentioned

before that the initial FRI toolbox was implemented in the

MATLAB environment, in which researchers have opened and

accessed the FRI source code, however, the use of source code

still demands in-depth knowledge (i.e. fuzzy rule interpolation

methods), and thus does not perform the same purpose as

toolbox in terms of obtaining the material simply available for

users from various backgrounds.

The FRI Toolbox is a set of FRI functions, which can be run

under MATLAB. It is easy to use and beneficial tool for

demonstration and research purpose, but in the real application

could be troublesome. It is based on the MATLAB, that is

restricted in terms of its availability (MATLAB is ruled to

license fees) and its user base. These constraints, limit the

appropriation practicable of the current MATLAB FRI toolbox.

For this purpose, a new developer framework based on

OCTAVE environment which includes FRI methods has been

introduced.

The FRI toolbox presented in this paper is based on the

openly available OCTAVE language. As regarded, OCTAVE

gives the advantage of not only being openly available but

importantly that it, as a language is accessible to users from a

broad variety of backgrounds. Moreover, the benefit of high-

level mathematical languages such as OCTAVE and MATLAB

provides built-in primitives for representing and manipulating

vectors and matrices, which can be used to directly represent

and manipulate fuzzy sets. Meanwhile, these languages provide

rich built-in graphical abilities for 2D and 3D plotting, which

can be utilized to represent fuzzy sets.

III. FRI TOOLBOX FEATURES

The OCTAVE FRI toolbox has several associations with the

MATLAB FRI toolbox. This is natural as both FRI toolboxes

perform determined FRI concepts and methods. The similarity

between both languages, nevertheless, has the distinct benefit

of greatly facilitating the use of either toolbox for researchers.

The resemblance based on the essential FRI concept between

both OCTAVE and MATLAB FRI toolboxes will be illustrated

in III-A, followed by a basic overview of the main structure of

FIS and OBS data files in III-B and the main function of the

FRI displays in III-C.

A. The MATLAB and OCTAVE Program Languages

MATLAB and its toolboxes, including fuzzy logic and Fuzzy

Rule Interpolation (FRI) toolbox have become in fact standards

in both university and production environments for engineering

computation and design. For many potential MATLAB users,

however, the cost is prohibitive and the license too restrictive.

To meet the needs of these users, an opensource equivalent of

MATLAB, called OCTAVE, was written and shared under the

GNU Public License [3]. OCTAVE is one of the high-level

programming languages which aimed to work on numerical

computations. It was developed to be a simple and interactive

environment in comparison with other softwares, such as

FORTRAN. OCTAVE is enhanced by usercontributed

packages managed by OCTAVE-Forge [4]. The packages

provide a wide-ranging of functionality.

One of the essential features of OCTAVE is its compatibility

with MATLAB since it uses the same syntax used in MATLAB

and it can run MATLAB m-files [5]. Programmers can find

some differences between OCTAVE and MATLAB since

OCTAVE parser allows some syntax, that MATLAB does not,

such as quotes, where single and double quotes are supported

in OCTAVE, but only single quotes are used in MATLAB.

Another kind of differences is that OCTAVE supports C-style

auto-increment and assignment operators where MATLAB

does not.

Comments in MATLAB are written after % while in

OCTAVE you can use both % and #. In MATLAB the control

blocks (while, if and for) as well as the functions delimiter all

finish with ”end”, while in OCTAVE you can also use

”endwhile”, ”endif”, ”endfor” and ”endfunction” respectively.

In MATLAB the not equal to operator is ”=” while in OCTAVE

”!=” is also valid. MATLAB does not accept increment

operators such as ”++” and ”–”, while OCTAVE accepts them.

Therefore, this free, open-source implementation of established

techniques in a MATLAB-like environment provides a

practical alternative for many students and researchers.

While there is no difference between OCTAVE and

MATLAB, in terms of the scope of the implementation the

current state of the OCTAVE FRI toolbox is similar to the

MATLAB FRI toolbox in terms of fuzzy rule interpolation

type-1, however, the OCTAVE FRI toolbox. For the majority

of the type-1 functionality, one can establish a comparison

between the functions implemented in the OCTAVE FRI

toolbox and those in the MATLAB FRI toolbox as is expected

because of the essential FRI concept.

B. The FIS and OBS Structure

Because the FIS Structure is central to the OCTAVE fuzzy

logic toolbox, the toolbox’s FIS structure is designed to

correspond to the data files in the MATLAB fuzzy logic

toolbox. The FIS and OBS structure as implemented by

MATLAB FRI. The OCTAVE fuzzy logic toolbox uses the

same structure for its FIS and OBS. Fig. 1 shows the main

structure of the FIS and OBS, also shows the member of the

structure that describes the membership functions ”paramsy”,

which includes the membership values for the characteristic

points of the fuzzy sets in case of piecewise linear membership

functions.

Fig. 1. FIS and OBS Data Structure [1]

The FIS and OBS data files format of the membership

functions can be described as follows: (MF1=’A1;1’:’trapmf’, [3

8 12 17]![0 1 1 0]), (MF2=’A2;1’:’trimf’, [5 10 15]![0 1 0]), and

(F3=’B1;1’:’singlmf’, [10]![1]), where, trimf, trapmf and

singlmf refer to triangular, trapezoidal and singleton

membership functions respectively, the A1;1,A2;1 and B1;1 denote

the names of the membership functions, the values [10 20 30],

[4.5 5 5.5 6] and [0.46] denote to the characteristics points

(params) of the membership in universe of discourse, a new

parameter in fuzzy interpolation structure is called (paramsy)

that was represented by ![0 1 0], ![0 1 1 0] and ![1], this

parameter refer to the breakpoints of the characteristic points of

the antecedents, consequences and observation fuzzy sets.

C. Implementation of ievalfis

The function ”ievalfis” is the core of the FRI toolbox.

”ievalfis” evaluates a FIS and OBS files of FRI methods, and

for each set of inputs, ievalfis returns one or more crisp output

values. The function ”ievalfis” may be called as follows:

output=ievalfis(OBS, FIS, InterpolationType, Params);

The crisp input values are arranged in a matrix, called user

input above, in which each row represents one set of FIS inputs.

For an FIS that has M inputs, an input matrix of v sets of input

values will have the form:

The output is a matrix of crisp values in which each row

represents the set of outputs for the corresponding row of user

input. For an FIS that has M outputs, an output matrix

corresponding to the preceding input matrix will have the form:

The optional argument num-points specifies the number of

points over which to evaluate the fuzzy values. If not specified,

the default for some methods value of 101 or 501 in other

methods is used. Furthermore, to returning the crisp output

values, ievalfis returns its results based on the FRI method used.

These results may be plotted or further analyzed. The format of

the resulting output depends on the Fuzzy Interpolative System

(FIS) type used.

IV. FUZZY INTERPOLATIVE SYSTEM TYPES

This section presents a brief overview of different methods

and approaches that are used for fuzzy rule interpolation

concept. It also provides some relevant works related to the

application of using the FRI MATLAB toolbox.

The first FRI method (KH FRI) was proposed by Koczy and´

Hirota [6]. It was initially referred as ”linear interpolation”, the

KH FRI is based on linear interpolation of α-cuts of the fuzzy

sets, it applies linear interpolation for getting the conclusion for

both end points of each α-cuts of the observation, rule

antecedents and consequent fuzzy sets. The conclusion could

be calculated using the fundamental equation of the KH FRI

(1), which is based on the lower and upper fuzzy distances

between fuzzy sets [7].

dist(A∗,A1) : dist(A∗,A2) = dist(B∗,B1) : dist(B∗,B2)

(1)

where d refers to the Euclidean distance that could be used

between the fuzzy sets (A2, A2) and (B1, B2).

The upper and lower endpoints could be used to calculate the

distance between the conclusion and the consequent which

must be comparable to the upper and lower fuzzy distances

between observation and antecedents. It can be calculated by

(2):

(2)

A modification of the KH FRI is called (VKK FRI), it was

proposed by Vass et al. [8]. This method is also following α-cut

technique, where the conclusion is computed based on the

distance of the center points and the widths of the α-cuts,

instead of their lower and upper endpoints of the KH method as

shown in Fig.2.

Fig. 2. The Distance of the Center Point and Width in the VKK Method [8]

The stabilized KH (KHstab FRI) was proposed by Tikk et al.

[9] to handle and exclude the possible abnormal conclusion. For

calculating the fuzzy conclusion, this method applies the

reciprocal distance as weights between all the rule antecedents

and the observation for all the α-cuts. The universal

approximation property holds if the distance function is raised

to the power of the dimension of the input as shown by (3) and

(4).

(3)

(4)

Another approach of FRI methods is called the Modified

αCut based Interpolation (MACI) method [10]. The main idea

of this method is based on the vectors description of the fuzzy

sets for eliminating the abnormality problem in the conclusion.

The fuzzy set in this method could be described by two vectors

space, it can represent the left and the right flank of the αcut

levels where the abnormal consequent set is excluded. The

conclusion B∗ in this method could be determined by (5).

RB∗ = (1 − λcore)RB1 + λcoreRB2 (5)

Where,

The Conservation Relative Fuzziness (CRF) method was

introduced in [11] by Koczy, Hirota, and Gedeon. This method´

aims to obtain the conclusion based on determining the core of

conclusion C∗ based on computing the ratio distances between

fuzzy set of the antecedents (d1(A1,A2)) and consequences

(d1(B1,B2)) with the core length of c∗ of the observation as

shown in Fig.3. Therefore, the CRF technique determines the

fuzziness of the (left A1, right A∗) must be the same fuzziness

of the (left B1, right B∗), and similarity the fuzziness between

(left A∗, right A2) and (left B∗, right B2).

Fig. 3. The Ratio Distances Between Fuzzy Sets [11]

The IMUL method proposed by Wong, Gedeon and Tikk

[12], IMUL was introduced to avoid the abnormal conclusion

and improve the multidimensional α-cut (levels) based on the

fuzzy interpolation. This method was introduced to combine

between the features of MACI and CRF methods. The IMUL

method applied the vector description, it can describe the

characteristics points of the fuzzy sets through advantageous

the transformation feature of MACI method, and representing

the fuzziness of the input and output by CRF method. The

conclusion in the IMUL method is based on calculating the

left/right core (LC/RC) and flank (LF/RF) as using the

Equations (6) and (7):

LCB∗ = (1 − λcore).LCB1 + λcore.LCB2+

(λcore − λleft/right).(LCB2 + LCB1) (6)

(7)

The General Method (GM), it was published by Baranyi et

al. [13]. The GM method will adopt the characterization of the

position fuzzy sets to determine the reference points (core),

thus, the distance between the observation and antecedents

fuzzy sets can be calculated based on the reference points as

shown by Equation (8). The conclusion in this method could be

determined by two algorithms, the first one is based on the

fuzzy relation, which is to generate a new interpolated rule Ri :

Ai → Bi that positioned between rules R1 and R2, the position of

the new rule is the same position of the observation, thus, each

fuzzy set of the antecedents is used to produce the new rule

which must be identical with the reference point of the

observation fuzzy set in the corresponding dimension.

d(A1,A2) = |RP(A2) − RP(A1)| (8)

The second one is based on the semantics of the relations,

which is the new rule could be specified as a part of the

extended rule of the approximate conclusion, as a conclusion of

the inference method is defined by determining this rule. In

many instances, there is no identical similarity between the rule

and the observation part, for this purpose, many techniques are

used to handle the mismatch by either the Transformation of the

Fuzzy Relation (TFR) technique or by Fixed Point Law (FPL).

The ScaleMove method was presented by Huang and Shen

[14], it follows the interpolation concept to handle the sparse

fuzzy rule bases. The ScaleMove method provides the abilities

to work with different fuzzy membership functions types. This

method is based on the Centre Of Gravity (COG) of the

membership functions as shown in Fig.4. It creates a new

central rule via two adjacent rules that are surrounding the

observation.

Fig. 4. Representative Value of a Triangular and Trapezoid Fuzzy Sets [14].

This ScaleMove method takes two steps to get the

conclusion, the first step is to produce a new central rule (A0 →

B0) is produced within the existing surrounding rules between

observation (A∗ : A1 → B1,A2 → B2) through to apply the

Equation (9):

(9)

The second step is to calculate the A0 similarity degree

between fuzzy sets (A0 and A∗) that is transforming B0 to B∗ with

the desired degree of similarity by the scale and move

transformations.

V. FUZZY RULE INTERPOLATION MATLAB TOOLBOX AND

RELATED WORKS

In [15], the fundamental concepts of a Fuzzy Rule

Interpolation-based (FRI) Reinforcement Learning (RL)

method called FRIQ-learning were discussed with benchmarks.

The interpolation within the knowledge-base allows the

removal of less important, unnecessary information, while still

keeping the system functional. A Fuzzy Rule Interpolation

based (FRI) RL method called FRIQ-learning is a method

which possesses this feature. FRIQ-learning is also suitable for

knowledge extraction. The FIVE FRI method was used By

handling the antecedent and consequent fuzzy partitions of the

fuzzy rule-base as scaling functions (weighting factors), which

turns the fuzzy interpolation to scale crisp interpolation. The

implementation of the FIVE FRI is also appearing in the FRI

toolbox [2].

The authors in [16] give a brief introduction to the FRI

methods and description of the refreshed and extended version

of the original fuzzy rule interpolation MATLAB toolbox.

The methods used in the FRI toolbox (KH, KH Stabilized,

MACI, IMUL, CRF, VKK, GM, FRIPOC, LESFRI, and

SCALEMOVE) were tested to compare them according to the

abnormality and linearity criteria, based on different numerical

benchmark examples.

The authors in [17] introduced the benefits of the FRI in the

Intrusion Detection Systems (IDS) application area, for the

design and implementation of the detection mechanism for

Distributed Denial of Service (DDOS) attacks. The

performance of the FRI-IDS application was compared to other

common classification algorithms (support vector machine,

neural network, random forest and decision tree) used for

detecting DDOS attacks on the same open-source test-bed

environment. According to the results, the overall detection rate

of the FRI-IDS is in pair with other methods. Consequently, the

FRI inference system could be a suitable approach to be

implemented as a detection mechanism for IDS; as it effectively

decreases the false positive rate value.

In [18], authors introduced a detection approach for defining

abnormality by using the Fuzzy Rule Interpolation (FRI)

methods with Simple Network Management Protocol (SNMP)

Management Information Base (MIB) parameters. The

implemented experiments were performed using Matlab and

the Fuzzy Rule Interpolation Toolbox (FRIT) [2]. The FIVE

method was chosen as the inference reasoning of the proposed

detection approach.

Authors in [19], analyzed equations and notations related to

piece-wise linearity property, which is aimed to highlight the

problematic properties of the KH FRI method to prove its

efficiency with piece-wise linearity condition. The study

presented in the benchmark examples can be served as a

baseline for testing other FRI methods against situations in

which the linearity condition for KH FRI is not fulfilled. In the

study, the FRI Toolbox was used to test the benchmark

examples for different FRI methods.

VI. FUZZY RULE INTERPOLATION OCTAVE (OCTFRI)

TOOLBOX

A. General description

The OCTAVE FRI toolbox is aimed to commonly giving at

least the same set of features as it exists in the MATLAB FRI

toolbox. Being an open-source toolbox, it is hoped that in the

overall feature richness and functionality of the toolbox will be

increased in time through the open access contribution.

The OCTFRI toolbox is the initial version of FRI techniques

based on OCTAVE language, which includes FRI functions to

evaluate FISs and OBSs files from the command line and

OCTAVE scripts, which is done by read FISs and OBS files

and produce a graphical output of both the membership

functions and the FIS output. The main goal of the OCTFRI

toolbox is to unify different fuzzy interpolation methods. The

current version supports twelve FRI methods (KH,

KHstabilized, MACI, IMUL, CRF, FIVE, VKK, GM, FRIPOC,

LESFRI, VEIN, and ScaleMove (note that ScaleMove style

inference is currently supported only in the OCTFRI toolbox)).

Nevertheless, the number of included techniques is still

growing. The toolbox is available for download under GNU

general public license from website [2]. As part of describing

the FRI inference systems functionality, a wide variety of forms

of membership functions are supported similar to those

currently provided by MATLAB such as singleton (singlmf),

triangle (trimf), trapezoid (trapmf), polygon (polymf).

Additionally, currently, the common forms of conjunction,

disjunction, implication and aggregation operators are

supported (including, minimum, maximum, product and

probabilistic OR). The number of rules is not restricted. There

are some restrictions to use FRI toolbox, only convex and

normal fuzzy sets are allowed (see [20]). In case of GM the

allowed set types are: singleton, triangle, trapezoid. Fig.5

describes the general structure of OCTFRI toolbox that could

be used to run the OCTFRI toolbox and to evaluate the current

FRI methods.

Fig. 5. The General Structure of OCTAVE FRI Toolbox

B. Parameters of the FRI methods by OCTFRI toolbox

The FRI method parameters could be defined by the main file

of the OCTFRI toolbox ”OCTFRI.m”. Regarding the KH, VKK

and KHstabilized methods which use two types of parameters,

the first parameter is ”breakpoints” (0 or 1) is considered as a

default parameter and denoted the α levels defined by the

breakpoints [0 1] of the fuzzy sets, the second one is

”userdefined”, which the user specifies the number of α levels

that will be distributed uniformly in the interval [0,1], for

example:

params.InterpolationType=’KH’; params.AlphaLevels.Type=’breakpoints’; or

params.AlphaLevels.Type=’userdefined’;

In case MACI and IMUL methods that used RPtype

(corecentre) parameter, which refer to the type of the reference

point of the fuzzy set, e.g. params.InterpolationType=’MACI’;

params.RPtype=’corecentre’. For FRIPOC and LESFRI

methods share the same parameters, where the FEAT-p

technique can take all fuzzy sets that belong to the partition with

different weight values. The type of the weighting factor and its

parameters can also be set by the user, e.g.

params.InterpolationType=’FRIPOC’;

params.NumOfPoints=501; params.RPtype=’corecentre’;

params.NumOfpCuts=61;

params.SetInterpolationWeight.p=2;

params.ConsequentPositionWeight.p=2;

Most of FRI methods calculate multidimensional distances in

the Minkowski sense. The parameter w of the formula can also

be set by the user where default value is 2. The default values

of the FRI methods parameters are sufficient to show the

desired conclusion.

C. Usage of the OCTFRI toolbox and evolution an FIS and

OBS

The package of OCTFRI toolbox can be used from a

graphical interface or from the command line. The current

version of the OCTFRI is simple and easy to use, which

contains all buttons of FRI methods, loading data files and

interpolation testing as shown in Fig.6.

Fig. 6. The Main Screen of the OCTFRI Toolbox

OCTFRI toolbox can be begun by typing in the command

line with the command ”OCTFRI.m”. First, the location of FIS

and OBS data should be provided (see Fig.7), which can be

done through the standard file open dialogue box.

Fig. 7. Location of FIS and OBS Data Files

VII. EVALUATION A FIS AND OBS DATA FILES

Twelve separate functions of the FRI methods as presented

in Fig.6 (eight of which were highlighted in this paper KH FRI,

KHstab FRI, VKK FRI, ScaleMove FRI, MACI FRI, IMUL

FRI, CRF FRI, and GM FRI) and six example FIS and OBS

files are included in the toolbox. A FIS and an OBS files needs

to be selected to be evaluated by the FRI method. The inference

process starts by loading the FIS and OBS data and select one

of the FRI methods, then the conclusion B∗ could be shown by

pressing on the interpolation button (see Fig.6). The input and

output universes will be shown in two separate windows, each

including the same number of diagrams as the dimensions of

the input and output respectively.

A. Example 1: Evaluation of the KH, KHstab, VKK and the

ScaleMove FRI Method

Example 1 applies the FIS1 and OBS1 data files stored in an

OCTFRI folder, which is including one input, one output

dimensions, and only two fuzzy rules as shown in Fig.8. The

membership functions of the input and output universes are

triangular fuzzy sets. Example 1 is tested on the KH FRI [6],

the KH Stabilized FRI [9], the VKK FRI [8], and the

ScaleMove FRI [14]) methods as described in Figs. 9 and 10.

Fig. 8. A FIS1 and OBS1 Stored in a File.

Fig. 9. Antecedent Partitions and Observations for the First Example.

Fig. 10. The Consequent Partitions and Approximate Conclusions of the FRI

Methods For the First Example.

B. Example 2: Evaluation the MACI, CRF, IMUL and GM

FRI methods

Example 2 applies the FIS2 and OBS2 data files stored in an

OCTFRI folder, which is including two input, one output

dimensions, and only four fuzzy rules as shown in Fig.11. The

membership functions of the input and output universes are

triangular fuzzy sets. Example 2 is tested on the MACI FRI

[10], the CRF FRI [21], the IMUL FRI [12], and the GM FRI

[13]) methods as described in Figs. 12 and 13.

Fig. 11. A FIS2 and OBS2 Stored in a File.

Fig. 12. Antecedent Partitions and Observations For the Second Example.

VIII. CONCLUSIONS

This paper presented the initial version of the FRI toolbox

ported to the OCTAVE language, which is an open-source (free

license) software available under the (GPL). The OCTFRI

toolbox is compatible with MATLAB through packages and

syntax, and it can also run m files and make modifications

without restrictions. The OCTFRI toolbox is a freely available

public tool, which is designed to be a test-base for FRI methods

comparison and also offers a simple way for solving real-world

problems. The current OCTFRI toolbox implements twelve FRI

methods (KH, KH Stabilized, VKK, MACI, IMUL, CRF,

FIVE, GM, LESFRI, FRIPOC, VESI and ScaleMove). The

SclaeMove method was added as a new inference method to the

OCTAVE FRI. For demonstrating the usage of the OCTFRI,

the results of two FIS and OBS data files were introduced in

this paper to evaluate the conclusion of the KH, KH Stabilized,

VKK, ScaleMove, MACI, CRF, IMUL and GM FRI methods

by the OCTFRI toolbox.

ACKNOWLEDGMENT

The described study was carried out as part of the EFOP-

3.6.1-16-00011 Younger and Renewing University - Innovative

Knowledge City - institutional development of the University

of Miskolc aiming at intelligent specialization project

implemented in the framework of the Szechenyi 2020 program.

The realization of this project is supported by the European

Union, co-financed by the European Social Fund.

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